Question

The equation of a line passing through $(-2,-4)$ and perpendicular to the line $3x-y+5=0$ is:

• A. $3y+x-8=0$
• B. $3x+y+6=0$
• C. $x+3y+14=0$
• D. None of these

Answer 1

The correct option is C

$x+3y+14=0$

Determine the equation of the line :

Let the required line be $AB$.

Given that: $AB$ passes through $(-2,-4)$ and $AB$ is perpendicular to $3x-y+5=0$.

therefore, Slope of $3x-y+5=0$ is given as:

$\begin{array}{rcl}& \Rightarrow & 3x-y+5=0\\ & \Rightarrow & y=3x+5\\ \therefore \mathrm{Slope}orm& =& 3\end{array}$

therefore, the Slope of $AB$ $=-\frac{1}{3}$ [Since, $m_1\times m_2=-1$, for lines perpendicular to each other]

Thus, the Equation of $AB$ is obtained as:

$\begin{array}{rcl}y-(-4)& =& -\frac{1}{3}(x-(-2\left)\right)\\ & \Rightarrow & 3(y+4)=-(x+2)\\ & \Rightarrow & 3y+12=-x-2\\ & \Rightarrow & x+3y+14=0\end{array}$

Hence, the correct answer is Option (C).